Calibration of a partially symmetric fixture

ABSTRACT

A method useful for the characterization of a fixture splits a partially symmetric THRU structure into portions which may then be mathematically removed from both ports of a 2-port measured structure, leaving only the desired device under test (DUT).

CROSS REFERENCE TO RELATED APPLICATIONS

The subject application claims priority from U.S. Provisional Patent Application Ser. No. 60/916,872, entitled, CALIBRATION OF A PARTIALLY SYMMETRIC FIXTURE (Kan Tan.), filed 9 May 2007, the entire contents of which are herein incorporated by reference.

FIELD OF THE INVENTION

The subject application concerns, in general, the field of test and measurement instruments, and in particular, concerns characterizing partially symmetric test fixtures.

BACKGROUND OF THE INVENTION

PCT patent application serial number PCT/US07/75485, CALIBRATION OF A MIRROR-SYMMETRIC FIXTURE (Doubrava, et al.) (hereinafter Doubrava '485), herein incorporated by reference, introduces a method for the characterization of a symmetric fixture, hereinafter called SymmetriCal. The SymmetriCal method (Doubrava '485) splits a symmetric THRU structure into mirrored Half-fixtures which may then be mathematically removed from both ports of a 2-port measured structure, leaving only the probe (i.e., the desired device under test (DUT)). What is needed is a method that can handle partially-symmetric fixtures.

SUMMARY OF THE INVENTION

A partial symmetric fixture is characterized with a single 2-port S-parameter measurement. The mathematical process splits the fixture into two partially symmetric half-fixtures, completely describing each half in terms of 2-port S-parameters.

BRIEF DESCRIPTION OF THE DRAWING

FIG. 1 shows an example of a partially symmetric fixture.

FIG. 2 shows another example of a partially symmetric fixture.

DETAILED DESCRIPTION OF THE EMBODIMENTS

The subject invention is an enhanced method which can handle partially symmetric fixtures. One example of partially symmetric fixture 100 is shown in FIG. 1, where the fixture is mostly symmetric, except for the inter-connectors 110, 120 and 116, 126 which are of two different types. The different connectors at the two sides may facilitate the through (THROU) calibration. Test fixture 100 includes a first trace 112 extending from a first connector 110 through a connection pad 114 to a second connector 116, and a second trace 122 extending from a third connector 120 through a second connection pad 124 to a fourth connector 126.

The second example of partially symmetric fixture 200 is shown in FIG. 2, where the fixture is less symmetric than the one in FIG. 1. Elements in FIG. 2 bearing similar reference numerals to those of FIG. 1 serve the same purpose, and need not be described again. In FIG. 2, only the connection pads 214, 224 and their neighboring area are symmetric.

The extended method of the subject invention, called Partial SymmetriCal, can handle fixtures satisfying the partial symmetry requirement. The term “partial symmetry”, as used herein means that the junction section between two half sides (LEFT and RIGHT Portions) is symmetric.

The pad areas shown in FIG. 1 and FIG. 2 are symmetric, so the test fixtures in FIG. 1 and FIG. 2 satisfy partial symmetry requirements. But they are not completely symmetric as required by Doubrava '485 (i.e., SymmetriCal™).

Less strict requirements in accordance with the method of the subject invention (which may be called, Partial SymmetriCal) provide more flexibility for fixture designs. For test fixtures that are supposed to be symmetric, the Partial SymmetriCal provides a means to check how good the symmetry assumption is.

Calibration of Partially Symmetric Fixtures

A partial symmetric fixture is characterized with a single 2-port S-parameter measurement. The mathematical process splits the fixture into two partially symmetric half-fixtures, completely describing each half in terms of 2-port S-parameters.

Measurement of a device under test (DUT) embedded between the half-fixtures can be easily de-embedded using the Half-fixture

S-parameters, or equivalently, T-parameters.

The partially symmetric fixture F and its components X and Y can be characterized in terms of S-parameters:

$\begin{matrix} {{Sx} = \begin{pmatrix} {Sx}_{11} & {Sx}_{12} \\ {Sx}_{21} & {Sx}_{22} \end{pmatrix}} \\ {{Sy} = \begin{pmatrix} {Sy}_{11} & {Sy}_{12} \\ {Sy}_{21} & {Sy}_{22} \end{pmatrix}} \\ {{Sf} = \begin{pmatrix} {Sf}_{11} & {Sf}_{12} \\ {Sf}_{21} & {Sf}_{22} \end{pmatrix}} \end{matrix}$

The partial symmetric constraints is reflected in the model as Sx₂₂=Sy₁₁  (1)

The reciprocity constraints applied to each component X, Y as well as whole fixture F yields: Sx₁₂=SX₂₁ Sy₁₂=SY₂₁ Sf₁₂=Sf₂₁  (2)

The S-parameters of X, Y and F are related by

$\begin{matrix} {\begin{bmatrix} {Sf}_{11} & {Sf}_{12} \\ {Sf}_{21} & {Sf}_{22} \end{bmatrix} = \begin{bmatrix} {{Sx}_{11} + \frac{{Sx}_{12} \cdot {Sy}_{11} \cdot {Sx}_{21}}{1 - {{Sx}_{22} \cdot {Sy}_{11}}}} & \frac{{Sx}_{12} \cdot {Sy}_{12}}{1 - {{Sx}_{22} \cdot {Sy}_{11}}} \\ \frac{{Sy}_{21} \cdot {Sx}_{21}}{1 - {{Sx}_{22} \cdot {Sy}_{11}}} & {{Sy}_{22} + \frac{{Sy}_{21} \cdot {Sx}_{22} \cdot {Sy}_{12}}{1 - {{Sx}_{22} \cdot {Sy}_{11}}}} \end{bmatrix}} & (3) \end{matrix}$

In the equation (3), Sf₁₁, Sf₁₂, Sf₂₂ can be obtained through two port measurements using a Vector Network Analyzer (VNA) or a Time Domain Reflectometer (TDR) on the whole fixture F; Sx₁₁ and Sy₂₂ can be obtained using the time domain gating method described in Doubrava '489.

Only three independent variables Sx₁₂, Sy₁₂, Sx₂₂ are unknown in (3). These three unknown variables can be resolved from three independent equations in (3) as following,

$\begin{matrix} {\frac{{Sx}_{12} \cdot {Sy}_{11} \cdot {Sx}_{21}}{1 - {{Sx}_{22} \cdot {Sy}_{11}}} = {{Sf}_{11} - {Sx}_{11}}} & (4) \\ {\frac{{Sx}_{12} \cdot {Sy}_{12}}{1 - {{Sx}_{22} \cdot {Sy}_{11}}} = {Sf}_{12}} & (5) \\ {\frac{{Sy}_{21} \cdot {Sx}_{22} \cdot {Sy}_{12}}{1 - {{Sx}_{22} \cdot {Sy}_{11}}} = {{Sf}_{22} - {Sy}_{22}}} & (6) \end{matrix}$

Multiplying (4) with (6) and dividing square of (5) yields

$\begin{matrix} {{Sx}_{22} = {\pm \sqrt{\frac{\left( {{Sf}_{11} - {Sx}_{11}} \right)\left( {{Sf}_{22} - {Sy}_{22}} \right)}{{Sf}_{12}^{2}}}}} & (7) \end{matrix}$

Plugging (7) into (4) and (6) respectively to get

$\begin{matrix} {{Sx}_{12} = {\pm \sqrt{\frac{\left( {{Sf}_{11} - {Sx}_{11}} \right)\left( {1 - {Sx}_{22}^{2}} \right)}{{Sx}_{22}}}}} & (8) \\ {{Sy}_{12} = {\pm \sqrt{\frac{\left( {{Sf}_{22} - {Sy}_{22}} \right)\left( {1 - {Sx}_{22}^{2}} \right)}{{Sx}_{22}}}}} & (9) \end{matrix}$

The signs in (7) (8) and (9) affect phase of S parameters. They can be resolved from time domain measurement and continuity of phase.

If Sx₂₂=0, then Sx₁₂, Sy₁₂ can not be computed from (8) and (9). Instead, they need to be resolved from Sx ₁₂ ·SY ₁₂=Sf₁₂  (10)

Extra knowledge of relation between Sx₁₂ and Sy₁₂ are needed to resolve them: for example, if THRU are symmetric, then Sx₁₂=SY₁₂

Or, if traces on left and right are uniform, but the trace in X side is twice as long as the trace in Y side, then Sx ₁₂ =Sy ₁₂ ·Sy ₁₂

Combining the relation between Sx₁₂ and Sy₁₂ with (10), Sx₁₂ and Sy₁₂ can be resolved.

For a completely symmetric fixture, which is considered in Doubrava '485, (1) will have two extra symmetric terms Sx₁₂=Sy₁₂ Sx₁₁=Sy₂₂

It can be verified that equations (3)-(10) with these two extra symmetric terms yield the same results as in Doubrava '485.

The subject invention (Partial SymmetriCal) can handle fixtures satisfying partial symmetry requirement, which is less strict than completely symmetric required by the SymmetriCal (Doubrava '485) method. For completely symmetric fixture, the Partial SymmetriCal yields the same result as SymmetriCal. For fixtures that are very close to symmetric, the Partial SymmetriCal provides a check on how symmetry it is, and can calibrate out asymmetry. The subject method (Partial SymmetriCal) is the super set of SymmetriCal; the Partial SymmetriCal involves more steps to gain more accurate calibration results. For the fixtures that are almost completely symmetric, if calibration efficiency is preferred over accuracy, then the SymmetriCal should be used; if accuracy is preferred over efficiency, then the Partial SymmetriCal should be used.

It is noted that the subject invention is also useful in combination with the teaching of U.S. patent application Ser. No. 12/117,461 CALIBRATED S-PARAMETER MEASUREMENTS OF A HIGH IMPEDANCE PROBE (Hagerup, et al.), herein incorporated by reference. 

1. A method for characterizing a partially symmetrical test fixture, comprising the steps of: providing a partially symmetrical test fixture; assigning a partial symmetric constraint of Sx₂₂=Sy₁₁; assigning a designation x to one portion of said test fixture having S-parameters Sx₁₁, Sx₁₂=Sx₂₁, and Sx₂₂ and a designation y to the remainder of said test fixture having S-parameters Sy₁₁, Sy₁₂ Sy₂₁ and Sy₂₂ for computation purposes; obtaining S-parameters Sf₁₁, Sf₁₂, and Sf₂₂ of said test fixture through two port measurements using a Vector Network Analyzer (VNA) or a Time Domain Reflectometer (TDR); obtaining S-parameters Sx₁₁ and Sy₂₂ through two port measurements using a time domain gating method; ${{solving} = {\pm \sqrt{\frac{\left( {{Sf}_{11} - {Sx}_{11}} \right)\left( {{Sf}_{22} - {Sy}_{22}} \right)}{{Sf}_{12}^{2}}}}};$ ${{solving} = {\pm \sqrt{\frac{\left( {{Sf}_{11} - {Sx}_{11}} \right)\left( {1 - {Sx}_{22}^{2}} \right)}{{Sx}_{22}}}}};\mspace{14mu}{and}$ ${solving} = {\pm {\sqrt{\frac{\left( {{Sf}_{22} - {Sy}_{22}} \right)\left( {1 - {Sx}_{22}^{2}} \right)}{{Sx}_{22}}}.}}$
 2. A method for characterizing a partially symmetrical test fixture, comprising the steps of: providing a partially symmetrical test fixture; assigning a partial symmetric constraint of Sx₂₂=Sy₁₁; assigning a designation x to one portion of said test fixture having S-parameters Sx₁₁, Sx₁₂=Sx₂₁, and Sx₂₂ and a designation y to the remainder of said test fixture having S-parameters Sy₁₁, Sy₁₂ Sy₂₁ and Sy₂₂ for computation purposes; obtaining S-parameters Sf₁₁, Sf₁₂, and Sf₂₂ of said test fixture through two port measurements using a Vector Network Analyzer (VNA) or a Time Domain Reflectometer (TDR); obtaining S-parameters Sx₁₁ and Sy₂₂ through two port measurements using a time domain gating method; ${{solving} = {\pm \sqrt{\frac{\left( {{Sf}_{11} - {Sx}_{11}} \right)\left( {{Sf}_{22} - {Sy}_{22}} \right)}{{Sf}_{12}^{2}}}}};$ wherein when Sx₂₂ is equal to zero and THRU traces of said fixture are symmetric then Sx₁₂·Sy₁₂=Sf₁₂ and Sx₁₂=Sy₁₂.
 3. A method for characterizing a partially symmetrical test fixture, comprising the steps of: providing a partially symmetrical test fixture; assigning a designation x to one portion of said test fixture having S-parameters Sx₁₁, Sx₁₂=Sx₂₁, and Sx₂₂ and a designation f to the remainder of said test fixture having S-parameters Sy₁₁, Sy₁₂ Sy₂₁ and Sy₂₂, and a designation f to the entire test fixture for computational purposes; assigning a partial symmetric constraint of Sx₂₂=Sy₁₁; obtaining S-parameters Sf₁₁, Sf₁₂, and Sf₂₂ of said test fixture through two port measurements using a Vector Network Analyzer (VNA) or a Time Domain Reflectometer (TDR); obtaining S-parameters Sx₁₁ and Sy₂₂ through two port measurements using a time domain gating method; ${{solving} = {\pm \sqrt{\frac{\left( {{Sf}_{11} - {Sx}_{11}} \right)\left( {{Sf}_{22} - {Sy}_{22}} \right)}{{Sf}_{12}^{2}}}}};$ wherein when Sx₂₂ is equal to zero and THRU traces of said fixture are uniform, then using the ratio between the physical length of the trace on x side and the physical length of the trace on y side to establish the relationship between Sx₁₂ and Sy₁₂.
 4. A method for characterizing a partially symmetrical test fixture, comprising the steps of: providing a partially symmetrical test fixture; assigning a designation x to one portion of said test fixture having S-parameters Sx₁₁, Sx₁₂=Sx₂₁, and Sx₂₂ and a designation y to the remainder of said test fixture having S-parameters Sy₁₁, Sy₁₂ Sy₂₁ and Sy₂₂, and a designation f to the entire test fixture for computational purposes; assigning a partial symmetric constraint of Sx₂₂=Sy₁₁; obtaining S-parameters Sf₁₁, Sf₁₂, and Sf₂₂ of said test fixture through two port measurements using a Vector Network Analyzer (VNA) or a Time Domain Reflectometer (TDR); obtaining S-parameters Sx₁₁ and Sy₂₂ through two port measurements using a time domain gating method; ${{solving}\mspace{14mu}{Sx}_{22}} = {\pm \sqrt{\frac{\left( {{Sf}_{11} - {Sx}_{11}} \right)\left( {{Sf}_{22} - {Sy}_{22}} \right)}{{Sf}_{12}^{2}}}}$ wherein when Sx₂₂ is equal to zero and THRU traces of said fixture are uniform, then using the ratio between the physical length of the trace on x side and the physical length of the trace on y side to establish the relationship between Sx₁₂ and Sy₁₂; wherein the step of using the physical length of the traces to establish the relationship between Sx₁₁ and Sy₁₂ includes a case in which said traces on said x portion of said test fixture are twice as long as said traces on said y side of said test fixture, then Sx₁₂ and Sy₁₂ exhibit a relationship of Sx₁₂=Sy₁₂·Sy₁₂; and when such relation between Sx₁₂ and Sy₁₂ is established based on said length ratio, then solving for Sx₁₂ and Sy₁₂ by use of Sx₁₂·Sy₁₂=Sf₁₂. 